Slope Stability

If the ground surface is not horizontal, a component of gravity will tend to move the soil downwards.

How slope failure will occur : If the driving force can overcome the resistance offered by the surrounding material along a rapture surface, slope failure will occur.

Slope stability analysis involves comparison of the developed shear stress along the most likely rapture surface and the shear strength of the soil.

 

 Factor of safety against sliding

(1) with respect to shear strength


where,
tau = shear strength of the soil (tau = S)
tau d = developed shear strength of the soil 

Note : phi' > phi' d and C' > C'd

How to determine actual failure plane,
- Determine several FOS for arbitrary failure planes
- Which gives the lowest FOS is the failure plane or potential plane or most critical plane

FOS > 1 no land slide occur
FOS < 1 failure will occur

Factor of safety can also be defined with respect to cohesion (Fc') or with respect to friction (Fphi').

(2) with respect to cohesion


where,
Cd' = developed cohesion

(3) with respect to friction


where,
phi d ' = developed friction angle

Stability of infinite slopes - Without seepage

Let's first consider an infinite slope having angle beeta, and assume that there is no pore water pressure in soil mass. Consider a failure of the slope along a plane parallel to the surface of the slope at a depth H.

 

Note : to find the critical depth, find H when Fs = 1.

For granular soils C' = 0, therefore Fs = tan phi' / tan beeta. This indicated that, in an infinite slope in sand, the value of Fs is independent of the height (H) and the slope is stable as along as beeta < phi'

Note : While slope excavation the maximum slope (in C' = 0 soils) we need to maintain is equal to the friction angle

Fs = 1 and C' = 0,
Fs = tan phi ' / tan beeta
beeta = phi'

If the soil processes cohesion and friction, the depth of the plane along which critical equilibrium occurs may be determine by substituting Fs = 1 and H = Hcr into the equation.

Hcr = Maximum wedge height we can maintain


 

Stability of infinite slopes - With seepage

 
Example :
A infinite slope is having a slope angle of 15 degrees, the wet unit weight, saturated unit weight, friction angle, cohesion are 18, 20, 20 and 10 respectively. Estimate the factor of safety of the slope. (thickness = 10m)

1. if the water table is at a significant lower level below the slope surface, and
2. if the water table is at the ground surface level

Answers :

1). if the water table is at a significant lower level below the slope surface


 Fs = 10/(18x10xcos15^2xtan15) + tan20 / tan15 = 1.58


2). if the water table is at the ground surface level

Fs = 10/(20x10xcos15^2xtan15) + (20-9.81)tan20/20xtan15 = 0.89